One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

• Autorzy: Veronique Lierde
• Języki publikacji: EN

Abstrakty

EN

Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic transform of R, if and only if the degree coefficient d(A v; v) is 1. We then give a criterion for R to be regular.

Słowa kluczowe

EN

Degree function; Rees valuation; 2-dimensional rational singularity

Kategorie tematyczne

• 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
• 13H05: Regular local rings
• 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1349-1353

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Veronique Lierde

• Al Akhawayn University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0095-y